Framed submanifold

Definition

A framed submanifold of a differential manifold is a submanifold along with a framing of its normal bundle, i.e. a global choice of trivialization for the normal bundle.

Not every submanifold of a differential manifold can be framed. In fact, a submanifold can be framed iff it has trivial normal bundle. Such submanifolds are termed framable submanifolds.